Electronic structure calculations for YH3 within the local density approximation result in a metallic ground state with the bands at the Fermi energy overlapping by more than 1 eV, whereas a band gap of 2.8 eV is deduced from optical experiments. Here, we report the results of parameter-free GW calculations which predict a fundamental gap of 1 eV. When we take into account electric dipole matrix elements a large optical gap of almost 3 eV is obtained. A combination of photoemission and inverse photoemission spectroscopy could test the prediction of a small fundamental band gap.